Wormholes in spacetime and their use for interstellar travel
Michael S. Morris · Kip S. Thorne
Summary and citation · read the original at the source
In one page
Michael Morris and Kip Thorne, both at Caltech, wrote this for the American Journal of Physics as a teaching exercise in elementary general relativity, and it changed the field. They begin by touching base with Carl Sagan’s novel Contact, which they note treats such travel in a manner that accords with the best 1986 knowledge of the laws of physics. Then they set out the objections to using black holes or Schwarzschild wormholes for the purpose, and present something new: a class of exact solutions of the Einstein field equations describing wormholes a human being could in principle pass through. The decisive property is that the throat carries no horizon. Impose that, and the field equations dictate what the throat must be made of — material under a radial tension of roughly the pressure at the centre of the most massive neutron star, scaled by twenty kilometres over the throat’s circumference, squared — and that tension must exceed the material’s own mass-energy density. Nothing known behaves that way.
Why it matters hereThis is the paper that made metric engineering an ordinary calculation rather than a genre, and it is where chapter 4 gets its central discipline: the geometry is free, the material is the whole problem — which is exactly why chapter 2’s question about what the vacuum can be made to do is the load-bearing one.
What it claims
01A new class of solutions of the Einstein field equations describes wormholes that, in principle, could be traversed by human beings — rapid interstellar travel by spacetime wormhole set out in a way that works as elementary general relativity.Abstract; the traversable-wormhole metric
Published and peer-reviewed02Black holes and Schwarzschild wormholes will not serve for this purpose, and the paper gives many objections to their use. The property that matters is that a traversable wormhole must possess a throat at which there is no horizon.Abstract; objections to black holes and Schwarzschild wormholes
Published and peer-reviewed03That no-horizon condition, together with the field equations, places an extreme constraint on the material generating the wormhole’s spacetime curvature: at the throat that material must possess a radial tension of magnitude roughly the pressure at the centre of the most massive neutron star, multiplied by twenty kilometres squared and divided by the throat circumference squared.Abstract; the throat constraint
Published and peer-reviewed04That tension must exceed the material’s density of mass-energy. No known material has this property, and such material would violate all the energy conditions that underlie several deeply cherished theorems in general relativity.Abstract
Published and peer-reviewed05The existence of such material cannot be firmly ruled out, and quantum field theory gives tantalizing hints that it might in fact be possible — which is precisely where the question passes from geometry to the physics of the vacuum.Abstract, closing sentence
What to watch06The transit itself is not a question of speed. Because the connection is through the wormhole’s throat rather than through the intervening space, what the solution engineers is the distance between two points, and the paper presents that as a legitimate exercise for a general relativity class rather than as a curiosity.Title and Abstract; the paper’s framing as a teaching tool
Published and peer-reviewed
The way in
https://doi.org/10.1119/1.15620Published by the American Association of Physics Teachers and copyrighted, so this page carries a summary; the abstract is open at the publisher and the record is indexed at INSPIRE-HEP and NASA ADS.
How to cite it
Michael S. Morris, Kip S. Thorne (1988) Wormholes in spacetime and their use for interstellar travel. doi:10.1119/1.15620
Where it sits in the curriculum
The metric, warp drives and wormholesWhat the vacuum isThe unified picture